When (a, b, c)abc(a,\,b,\,c) is a Pythagorean triple, i.e. aaa, bbb, ccc
are positiveintegers, a+b-cabca\!+\!b\!-\!c must be an even positive
integer which we denote by 2⁢r2r2r. We get from (2) the equation

(c-a)⁢(c-b)= 2⁢r2,cacb 2superscriptr2(c\!-\!a)(c\!-\!b)\;=\;2r^{2},

whose factors on the left hand side we denote
by ttt and sss. Thus we have the linear equation system